Every baby is different: some prefer both breasts at a feeding, some like just one. You can certainly try burping and then offering the other breast, but don't sweat it either way. As long as he does nurse on both breasts fairly equally throughout the day (for your own comfort), it should be fine.
But don't assume that he'll go longer between feedings if you offer both breasts, because it won't necessarily happen. The breasts continually make more milk as the baby is nursing, so if he keeps sucking on one breast, he will keep getting milk. Offering the other will probably give him a faster flow, but otherwise he'll be getting the same amount either way. It sounds like he just prefers one breast per feeding, and there's nothing wrong with that. Basically, if it ain't broke don't fix it!
Joan 39, single mama by choice to 10yo boy and 7yo girl